You may need to use the appropriate appendix table or technology to answer this question. According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively. (a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.) H0: Ha: (b) Using the sample from the 65 bottles, what is the test statistic? (Round your answer to three decimal places.) Using the sample from the 65 bottles, what is the p-value? (Round your answer to four decimal places.) p-value = (c) At α = 0.05, what is your conclusion? Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (d) Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: Find the value of the test statistic. (Round your answer to three decimal places.) State the critical values for the rejection rule. Use α = 0.05. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic ≤ test statistic ≥ State your conclusion. Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Question

You may need to use the appropriate appendix table or technology to answer this question.

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.

(a)

Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)

H₀:

H_a:

(b)

Using the sample from the 65 bottles, what is the test statistic? (Round your answer to three decimal places.)

Using the sample from the 65 bottles, what is the p-value? (Round your answer to four decimal places.)

p-value =

(c)

At α = 0.05, what is your conclusion?

Reject H₀. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Reject H₀. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H₀. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H₀. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

H_a:

Find the value of the test statistic. (Round your answer to three decimal places.)

State the critical values for the rejection rule. Use

α = 0.05.

(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤ test statistic ≥

State your conclusion.

Reject H₀. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Reject H₀. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H₀. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Do not reject H₀. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.